Highlights
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The minimum number of turbine revolutions in order to obtain a converged solution: 20–30 revolutions.
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The minimum distance from the turbine center to the domain inlet and outlet: 10D each (D: turbine diameter).
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The minimum domain width (maximum blockage ratio): 20D (5%).
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The minimum azimuthal increment dθ: 0.5°.
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The minimum requirements are identified for a lowsolidity VAWT at a moderate tip speed ratio with a chordbased Re > 10^{5}.
Abstract
Accurate prediction of the performance of a verticalaxis wind turbine (VAWT) using Computational Fluid Dynamics (CFD) simulation requires a domain size that is large enough to minimize the effects of blockage and uncertainties in the boundary conditions on the results. It also requires the employment of a sufficiently fine azimuthal increment (dθ) combined with a grid size at which essential flow characteristics can be accurately resolved. The current study systematically investigates the effect of the domain size and azimuthal increment on the performance of a 2bladed VAWT operating at a moderate tip speed ratio of 4.5 using 2dimensional and 2.5dimensional simulations with the unsteady Reynoldsaveraged NavierStokes (URANS). The grid dependence of the results is studied using three systematically refined grids. The turbine has a low solidity of 0.12 and a swept area of 1 m^{2}. Refining dθ from 10.0° to 0.5° results in a significant (≈43%) increase in the predicted power coefficient (C_{P}) while the effect is negligible (≈0.25%) with further refinement from 0.5° to 0.05° at the given λ. Furthermore, a distance from the turbine center to the domain inlet and outlet of 10D (D: diameter of turbine) each, a domain width of 20D and a diameter of the rotating core of 1.5D are found to be safe choices to minimize the effects of blockage and uncertainty in the boundary conditions on the results.
Keywords
 Vertical axis wind turbine (VAWT);
 CFD;
 Guideline;
 Domain size;
 Azimuthal increment;
 Number of revolutions
Nomenclature
 A

swept area, H.D [m^{2}]
 BR

blockage ratio (D/W ) [−]
 c

blade chord length [m]
 C_{m}

instantaneous moment coefficient [−]
 C_{P}

power coefficient [−]
 C_{T}

thrust coefficient [−]
 CoP

pressure coefficient [−]
 D

turbine diameter [m]
 d_{c}

diameter of rotating core [m]
 d_{i}

distance to the domain inlet from turbine center [m]
 d_{o}

distance to the domain outlet from turbine center [m]
 d_{up}

upstream distance to the turbine center [m]
 dt

time step [s]
 dθ

azimuthal increment [°]
 F_{s}

safety factor [−]
 H

turbine height [m]
 L

domain length [m]
 M

moment [Nm]
 q

dynamic pressure [Pa]
 R

turbine radius [m]
 Re

chordbased Reynolds number [−]
 Re_{θ}

momentum thickness Reynolds number [−]
 Re_{geo}

Reynolds number from geometrical relations [−]
 T

thrust force [N]
 u

timeaveraged streamwise velocity [m/s]
 U

velocity magnitude [m/s]
 U_{∞}

freestream velocity [m/s]
 v

timeaveraged lateral velocity [m/s]
 W

domain width [m]
 W_{geo}

resultant velocity from geometrical relations [m/s]
 α_{geo}

geometrical angle of attack [°]
 γ

intermittency [−]
 λ

tip speed ratio, Ω.R/U_{∞} [−]
 ν

kinematic viscosity [m^{2}/s]
 θ

azimuthal angle [°]
 ρ

density [kg/m^{3}]
 σ

solidity, n.c/D [−]
 ω

specific dissipation rate [1/s]
 Ω

rotational speed [rad/s]
1. Introduction
Recently, verticalaxis wind turbines (VAWTs) have received growing interest for wind energy harvesting offshore [1] as well as in the urban environment [2]; [3]; [4] ; [5]. For offshore application this can be attributed to their scalability, reliability and low installation and maintenance costs, while for environments with frequent changes in wind direction such as urban environments their omnidirectional capability is their main advantage. However, due to a comparatively small amount of research on VAWTs in the last 23 decades, their performance is currently lower than that of their horizontalaxis counterparts. The current renewed interest has resulted in more research and further understanding of VAWT flow complexities. These complexities include dynamic stall [6] ; [7], flow curvature effects [8], bladewake interactions and unsteady 3D wake dynamics [9]. Increased understanding of the aerodynamics of VAWTs has enabled further optimization of their performance which has been conducted using lowto moderatefidelity inviscid modeling [10] ; [11], highfidelity viscous CFD simulations [12] ; [13] and wind tunnel tests [9].
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